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ACHIEVING HIGHER ORDER CONVERGENCE FOR THE PRICES OF EUROPEAN OPTIONS IN BINOMIAL TREES
Author(s) -
Joshi Mark S.
Publication year - 2010
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2009.00390.x
Subject(s) - binomial options pricing model , mathematics , convergence (economics) , binomial (polynomial) , order (exchange) , tree (set theory) , conjecture , trinomial tree , class (philosophy) , mathematical economics , econometrics , mathematical optimization , valuation of options , economics , mathematical analysis , combinatorics , statistics , computer science , finance , artificial intelligence , economic growth
A new family of binomial trees as approximations to the Black–Scholes model is introduced. For this class of trees, the existence of complete asymptotic expansions for the prices of vanilla European options is demonstrated and the first three terms are explicitly computed. As special cases, a tree with third‐order convergence is constructed and the conjecture of Leisen and Reimer that their tree has second‐order convergence is proven.